Another direction would be towards quasilinear equations, modeled for example on the \(p\) -Laplacian operator. The extensive literature on the gradient regularity cannot be summarized here, see for example the recent survey [1]} and [2]}. The case with strong first order terms (in particular beyond the natural growth) appears to be still an open research field [3]}, [4]}. Liouville theorems are known [5]}, hence we believe that the techniques presented here could yield new results in this direction.
